Solve this system by substitution: y = x - 4 and 3x + 2y = 22.

1. The first rule already gives y on its own, as y = x - 4. 2. Put x - 4 in place of y in the second rule: 3x + 2(x - 4) = 22. 3. Expand the bracket to get 3x + 2x - 8 = 22. 4. Collect the x terms to get 5x - 8 = 22, then add 8 to both sides to get 5x = 30. 5. Divide by 5 to get x = 6, then put that back into y = x - 4 to get y = 2. 6. Check in the second rule: 3 times 6 is 18, 2 times 2 is 4, and 18 plus 4 is 22. 7. Option D fits the first rule only, since 3 times 5 plus 2 times 1 is 17 rather than 22. 8. Option B also fits the first rule only, since 3 times 4 plus 0 is 12 rather than 22. 9. Option A swaps the two values, and 2 minus 4 is minus 2 rather than 6, so it fails the first rule as well. _Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_